The thickness of sheet glass produced by the float process is normally constant. For example, a head-up display for displaying information on the windshield of an automobile (herein below, referred to as “HUD”), however, requires glass having a non-uniform thickness in order to eliminate the generation of a double image when seen from a driver. Under such a circumstance, investigation has been made about a process for producing sheet glass having a concave shape, a convex shape or a tapered shape in section in a width direction orthogonal to the advancing direction of a glass ribbon (hereinbelow, referred simply to as the width direction at some explanations later on) (see, e.g. Patent Documents 1 and 2).